• East Asian mathematical journal
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• 제29권3호
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• pp.269-278
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• 2013

A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

• 충청수학회지
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• 제25권2호
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• pp.217-225
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• 2012

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh defines the probability of the fuzzy event using the probability. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• 한국지능시스템학회논문지
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• 제24권4호
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• pp.398-402
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• 2014

일반화된 삼각함수 퍼지집합은 삼각함수 퍼지수의 일반화이다. Zadeh([7])는 확률을 이용하여 퍼지이벤트에 대한 확률을 정의하였다. 우리는 정규분포와 지수분포를 각각 이용하여 실수 $\mathbb{R}$ 위에서 정규퍼지확률과 지수퍼지확률을 정의하고, 일반화된 삼각함수 퍼지집합에 대하여 정규퍼지확률과 지수퍼지확률을 계산하였다.

• 한국지능시스템학회논문지
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• 제22권2호
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• pp.212-217
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• 2012

확률공간 (${\Omega}$, $\mathfrak{F}$, $P$) 위에 정의된 퍼지집합을 퍼지이벤트라 한다. Zadeh는 확률 $P$를 이용하여 퍼지이벤트 $A$에 대한 확률을 정의하였다. 우리는 일반화된 삼각퍼지집합을 정의하고 거기에 확장된 대수적 작용소를 적용하였다. 일반화된 삼각퍼지집합은 대칭적이지만 함숫값으로 1을 갖지 않을 수 있다. 두 개의 일반화된 삼각퍼지집합 $A$와 $B$에 대하여 $A(+)B$와 $A(-)B$는 일반화된 사다리꼴퍼지집합이 되었지만, $A({\cdot})B$와 $A(/)B$는 일반화된 삼각퍼지집합도 되지 않았고 일반화된 사다리꼴퍼지집합도 되지 않았다. 그리고 정규분포를 이용하여 $\mathbb{R}$위에서 정규퍼지확률을 정의하였다. 그리고 일반화된 삼각퍼지집합에 대한 정규퍼지확률을 계산하였다.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2007년도 추계학술대회 학술발표 논문집
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• pp.183-186
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• 2007

We introduction some properties for fuzzy power function of performance of a test. First we define fuzzy type I error and type II error for the probability of the two types of error. And we show that an fuzzy error probability of one kind can only be reduced at cost of increasing the other fuzzy error probability.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.33-36
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• 2008

We introduce some properties for fuzzy binomial distributions with fuzzy valued probability. First we define fuzzy type I error and type II error for fuzzy relative frequency and agreement index. And we show that an fuzzy power function and fuzzy binomial frequency function for binomial proportion test.

• 동력기계공학회지
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• 제18권1호
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• pp.135-139
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• 2014

We propose some properties for fuzzy hypothesis test by fuzzy significance probability. First, we define fuzzy number data and fuzzy significance probability for repeatedly observed data with alternated error term. By the agreement index, we compare fuzzy significance probability with significance level and drawing conclusions the degree of acceptance and rejection by agreement index.

• 대한수학회논문집
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• 제21권2호
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• pp.385-395
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• 2006

We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.111-125
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• 1992

Since Zadeh's definition for probability of fuzzy event is presented, alternative definitions for probability of fuzzy event is suggested. Also various properties of these new definitions have been presented. In this paper it is our purpose to show the works continued by finding a natural definition of a fuzzy probability measure on an arbitrary fuzzy measurable space. Thus, the main process is to observe fuzzy probability measure to be qualified by weak axioms of boundary condition, monotonicity and continuity suggested by Klir (1988). Especially, we will show that these axioms are satisfied through in succession of modifications from the Yager's method.